Question

Which is larger, the H 1s orbital or the Li 1s orbital? Why? Which has the larger radius, the H atom or the Li atom? Why?

Short answer

The Li 1s orbital is smaller than the H 1s orbital due to the higher effective nuclear charge experienced by the Li 1s electron (3) compared to the H 1s electron (1). However, the Li atom has a larger atomic radius than the H atom because it has more electron shells.

Step-by-step solution

Understand the concept of effective nuclear charge

Effective nuclear charge (Zeff) is the net charge experienced by an electron in an atom due to the attractive force of the protons and the repulsive force of the other electrons present. It is the difference between the total nuclear charge (Z) and the shielding constant (S). Mathematically, it can be represented as: \(Z_{eff} = Z - S\)

Find the effective nuclear charge for the H 1s and Li 1s orbitals

For hydrogen (H), there is only one electron and one proton in the atom. Therefore, there is no shielding effect. The effective nuclear charge experienced by the H 1s electron is equal to the total nuclear charge, which is 1. For lithium (Li), there are three electrons and three protons in the neutral atom. The two 1s electrons shield the outermost 2s electron from the full nuclear charge, but since we are considering the 1s orbital, shielding is negligible because the other 1s electron cannot shield the electron in focus. The effective nuclear charge experienced by the Li 1s electron is approximately equal to the total nuclear charge, which is 3.

Compare the size of H 1s and Li 1s orbitals

The size of an atomic orbital is inversely proportional to the effective nuclear charge experienced by the electron occupying that orbital. Since the Li 1s electron experiences a higher effective nuclear charge (3) compared to the H 1s electron (1), the Li 1s orbital is smaller than the H 1s orbital.

Find the atomic radii of H and Li atoms

Atomic radii increase down a group and decrease across a period in the periodic table. Hydrogen and lithium are both in Group 1 (alkali metals), but lithium is in Period 2, whereas hydrogen is in Period 1. Lithium has more electron shells, resulting in a larger atomic radius.

Summarize the results

In summary, the H 1s orbital is larger than the Li 1s orbital due to the difference in effective nuclear charge. However, the atomic radius of the Li atom is larger than the H atom because it has more electron shells. The bigger orbital size for H 1s does not necessarily mean that the overall size of the hydrogen atom is larger than the lithium atom.

Key concepts

Atomic Orbitals

Atomic orbitals are regions of space around the nucleus where electrons are likely to be found. Each orbital can hold a specific number of electrons. For example, the 1s orbital can hold a maximum of two electrons.
The shape and size of these orbitals depend on the energy levels and the effective nuclear charge experienced by the electrons.

• The 1s orbital is the simplest and smallest, found closest to the nucleus.
• Higher energy orbitals like 2s and 2p are found further away from the nucleus.

In the case of the hydrogen and lithium atoms, the 1s orbital is being compared. Because electrons in orbitals closer to the nucleus experience a stronger pull from the protons, they become more compact. This is why the Li 1s orbital is smaller than the H 1s orbital despite the extra electrons in Li, due to increased effective nuclear charge.

Atomic Radius

Atomic radius is the measure of the size of an atom, typically from the center of the nucleus to the outer boundary of the surrounding cloud of electrons. It is influenced by:

• The atomic number, which indicates the number of protons in the nucleus.
• The number of electron shells around the nucleus.

Moving down a group in the periodic table results in an increased atomic radius. Each step down adds another electron shell, making the atom larger. On the other hand, moving across a period, the atomic radius decreases as the effective nuclear charge increases, pulling electrons closer to the nucleus.
For hydrogen and lithium:

• Hydrogen has a smaller radius since it resides in Period 1, with just one electron shell.
• Lithium, situated in Period 2, has a larger atomic radius due to its extra electron shell, even though it has a smaller orbital size for its 1s electron compared to hydrogen.

Shielding Effect

The shielding effect occurs when inner electrons block the full impact of the nuclear charge from being felt by outer electrons. This reduces the effective nuclear charge experienced by outer electrons. It is calculated by subtracting the shielding constant from the total nuclear charge:\[ Z_{eff} = Z - S \]Where:

• \( Z \) is the total nuclear charge.
• \( S \) is the shielding constant, representing the screening effect of inner-shell electrons.

In hydrogen, there is no shielding effect since it has only one electron. Conversely, in lithium, two 1s electrons reduce the influence of the positive nuclear charge on outer electrons. However, when considering the 1s orbital of Li, there is negligible shielding because we're focusing on electrons very close to the nucleus.
This variation in the shielding effect helps explain why different atoms and orbitals behave as they do, including atomic size and orbital shape differences.